Give some examples of evvo+;hnhlt:3 0(2c kcfa a:xucoc4ln0eryday vibrating objects. Which exhibit SHM, at least approximan u+fla c aok3(n2hl4xc;hcot:0:0vctely?

Is the acceleration of n(;lozw - un(nly c+,ga simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is apprp7de-vca7ly d/ i 4s0ob -+oijoximately simple i0 l7do4pabc-yv d/s+e jo7 -iharmonic.

Real springs have mass. Will the true period and frequency be large.,4 hk yvcc1ml)a z7csr or smaller than given by the equations s4v c,c a.7kcmyh)1zl for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double zf4jse1vy0 s*s.,2j*t m)wnwmo - ljithe maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then c mav j/4t9n2fkus bfmw27,u *is released. Describe the scale reading as a function of2m* tu sm 2vbj9f/f 7,ucaknw4 time.

If a pendulum clock is accurate at sea level, will it gain or lose time whe ps fgulzyx)g9 9v5d2mm- d-olj:2l0xn taken to higu -x2 d0slldy-v mmo )g9p9lx5 zgj2f:h altitude? Why?

A tire swing hanging fqejeytv,ki 9* e:*ne7 rom a branch reaches nearly to the ground (Fig. 11–48). How could 7 e9tjeeiqn:e*ky *, vyou estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pa:xjxvlgxw hhc h:)boeo9 ) zz84;2 a8fn at a c x) fhzhg8ow b :8jh4lv)xxo9zc2:a; eertain frequency?

Give several everyday examples iy di),dd (sw u:j.d;bof resonance.

Is a rattle in a car ever s ;2j( z)hf,l0dla0lpuyq 2jna resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sourceiz;o:x/ l i03 sp0xduh? Why or wdp;0ou:si x3i/hxz 0lhy not?

Explain the difference between the speed of a transve 8d-1su udgx ):+kagdcrse wave traveling down a cord and the speed of a tisa) x-ugk:gd8dud +1 cny piece of the cord.

Why do the strings usmmf *g60i yc.uyau:1p ed for the lowest-frequency notes on a piano normally have wire wrapped around fy ym6i*pma0:g1 uuc .them?

What kind of waves do you think will travel down a hoyu 34x7no x7jarizontal metal rod if you strike its end (a) verticalxa7nox7jy4 3u ly from above and (b) horizontally parallel to its length?

Since the density of air decreases with an in:s8 4 abr1.iclj oxzz4crease in temperature, but the bulk modulus B is nearly independent.bl4oajx1 cz48 rzsi: of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in aw0eqg x;j99dv eh d(t)mplitude as they travel away from the xh; et9d)9 w0jqv ged(source.

Two linear waves have the same amplitude and speed, and otherwise arowrovnds / hpwqtx32r8:9(h9e identical, except one has half the wavelength of the other. Which transmits more energy? By what factot(8 d:wr39 2s/9p noqhx ohwvrr?

When a sinusoidal wave crosses the boundary between two sections of cord as i:v ;/xtd*k00pst7 fqhfvgj3xn Fig. 11–33, the frequency does not change (although the wavelegj /xs;q3f:vk*xtf 0 h0tvd7pngth and velocity do change). Explain why.

If a string is vibrating in three segmw,flor/j5u*oig6d 4m, w.sjhpv sf/n7 i) z g*ents, are there any places you could touch it with a knife blade without disturbing thew6gvhfiwod.,gp/o,jn/7smr* uj5* l )4z isf motion?

When a standing wave exists on a string, the v0i e; ornaf);dwexfi*8b3py* ibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explai; 0eiio w3)a xdfr;* yfbnp*8en.

If we knew that energy was being transmitted from one pxv b ;yq b57(u2em6jujlace to another, how might we determine whether the energy was being carried by particles (majv( ejb5mqu y26ux 7b;terial bodies) or by waves?

  If a particle undergoes SHM with amplitude /rv(g:e+421 aw zp xdysixosc2 o99l d0.18 m, what is the total distance it travels in one perssx px e +o9ory4d9c(2wlda: igvz1/2 iod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is *t6-- seapcw h85 cm long when a weight of 180 N hangs from it. What is thece-sah -6tw*p “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car,bfz/icjm93x ,3u lrf compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car fb , zcfu/,mjx 9r33ligoes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs fromojiz; i;bz ;:qtr x o/0so3mp* it. (a) What is the tz0pz3 oi ;x:q;oo* /;smrijbspring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a m q/q*h2jf -ntc zp/sl *md,+goass of 0.60 kg is hung fro, d*ph-q 2/n+*z/qtsojmg flcm it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positio df wx:.k yc1ah,z(o6ln x of the mass in Fig. 11–2 at times t = 0kz d h,fy:(1 aw.6lcox,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s1h(0s 59, uxqkerg awz: 2uosk web. The web vibrates predominately with(s uzg ws:qo,2khe arxu0159k a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of6z(u r 1x dud*1ibb+cc a spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value zur1d+ *6d(ixb1c b ucof m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3. p z7b+ 8r 3oxeji3,aq.bxb8ut0 times per second with an ampl8,7tepbx+az.q8 o3jbr3xu bi itude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibriu0u;,a:)lqxb .wda of jm is the speed of a SHO half the maximum value:0)qu, aojfwba;x.l d ?$\approx$    A

A mass attached to the end of yg)2k /4pt ytoh7.gfn a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If thev*p8wxnh ; ,aq spring is stretched an additiona;,phavn xw8q *l 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with sph wd t9pb(zsny w3u933m0stk/w n.e i6ring stiffness constant k = 280 N/m and is executing simple harmonic motion. Wh( tn.bw wsshmw ni0z393e6utpy9kd/3en the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of hcx, 8ia: t-ns7lvm;y a toy popgun 0.200 m to “load” a 0.180-kg ball. Withycn:-7,ml axv;t8 his what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, f rt:d s):g:ldmrictionless surface is attached to one end of a spring; the other end is s :t::)gl ddrmfixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the +i)6pkhvp-wiy)v, q bequation x = 0.45cos6.4t where x is in meters and q),yw hipvv+ )- 6bpkit is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equ,;7 fyy8wo mcailibrium is the energy of a SHO half KE and half PE?m yc,8yoaf ;w7 ±    A

  If one vibration has 7.0 times the energy of 4b0wxjo871msmj1lu s a second, but their frequencies and masses are the sameoss8j71j0 xlw1mbu4m , what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lic.i: z1s ne-rs(ftt7 xght spring once every 0 (.sftz e7:c 1nit-rxs.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identi0t u8)+f oco5afbwf u(cal parallel vertical springs, each with spring stiffness constant k (Fig. 8o 0tuoff+ cw5fb()u a11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equatioj f+jwjd/pieqxf:35pw4jo(k-ak-l 8 n x = 0.38sin6.5t where x is in meters and t/jk: 5 i4lp ffdj(8wje-oq 3kj-wa+p x is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For e478e y rfnw6p9odnum 1ach, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal 64zng nqb*n.ul 3k4bx spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determineg.6 4bnub3q4xzn k* ln
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an amplitfjz2 k*50 q;y )iio(lli+vuujude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the e0yj l)q5iziliujfu+ ov 2 k*(;quilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with sprinx2gke2 2lij* lgsaqni * q))j1g stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a bxgf8nv95)k l fixed horizontal spring whose spring stiffness consk l9b5xn8f gv)tant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with m951 lgo3o jl o+eaxc2tass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the a1o5e o+o2j gct3llx9bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is 3gx0 fa0bbhbdau*/n/3 yoqwyub 1*0gits
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactli -;sdqdwyb br/k*0mn)z1k a;y one swing per second z-ib*/rdyb;0kd)1q nk ;aswm? (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is c. +tbq, pif2lmn80 2tmhd7)nd8 ddgt its period on Mars, where the acceleration of gravity is about 0.37 tha g)7mtnct8pb82 lhd+di02 , qdmd.fntt on Earth?    s

  What is the period of a simple pendult-ut+ett2 a8rk2izy 0um 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bwy r /h nj1w)n5uehg(jsx/u 76ob has a mass of 365 grams, and it is releas7u sjryx/n gwn(516hwe)/juhed at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s gv 6 , p zr*y5s2dj0it;mf6omrxs;m0vpendulum has a length of 0.9930 m. If the clock loses half a minute per m6zipsxsy ;,rmv*0 m562rto jv0;gdf day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxim (ydddex6 vj*ov24 1obtkix .6-fvu.yum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum osciq.jvz / 79) ,yisnspra6g6tmj: b+hlollates at a frequency of 2.5 Hz. At it is released from rest qzam7o r.6)l:6 gsjb/i9 jpn +,vythsstarting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his aiiig )y q,y :sv((hw*wnchored boat every 3.0 s. He measures the distance betwe *sywy(vq(g hi:)wi i,en two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a fn;w(b3cev 0l)6u q mv pmx*p:qrequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (comvbq ucv0wx6m(e* p:; m 3q)pnlpressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600,xyz -g p u+jagi83q m.(9pfsu kHz (kilohertz) and tragyqp.jum+up zaig-s , 893xf(vel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal tw6nm8sb8y: v waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastipqa9bid3 //aql:hvunv * *79q bq dv2yc modulus, but one is twice as dense as the other. In which rod will thendqb 3*/a*qlvi yh2vq:u 97bd9vpa/q speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretchb xbc 2.:uzlxym;.i1ued between two supports 28 m apart. If the tension in the cord is 150 N, howz1u ;.m .2yxbb:l icxu long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top o9 9d-w+y f5kyv ;o qfn1yjzog1f a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gonyf 1nqv-5ofjw dzkoy ;g+y991dola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just bel :0s1fs0bjofhow the surface of the sea. He hears the echo of the wave reflected from the f s0s0fb:1hjoocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earth1pi-ei c2 1bgolt (ptw.8c*gdquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where ttg i.(c8-b*p2g i1potw d1cl ehe disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal transver(ztk 6w,mtw:)oe6 jquse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actualut j,q)e m z6wk:(owt6ly include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensi9y o4gh9:us; 0k iir, wlk.cmvties, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from th,w:v.y oi;9ukg0 chlim4 9 ksre source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is me9iqn53q;4d+ u wvvmra g:7nmeasured to be rqi d 3qa7um5:gvw4vn9+ emn;$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portio 0h hac.b7m+din of the Earth, but b+idhm0ac7. hone is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have t4aadim ,.f- h4yjc h.jhe same frequency, but one transports three times the power of the other. What is the ratio of themd4c-h4.yh afa,jj i. amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move sxapk*v5 0 *+5dcpzwyup and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does thc 55s0pykzawvdx p**+e bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Skfw9 eysx(zrc7y1s ce:.71r ewetch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulseycrf.e y 1(cxw79 sse1e zw:r7s pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are7ud2k4dm s tm g i/;o)jg4th8p the frequencies gt dms7)u 2t kg8do 4ipmh/4;jof the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 2brc6k;0i z67uwfz, k3ot - dga94 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a s3bcz;gfwdt67-r zku, k 6a0i otanding wave.)    Hz

  A particular string r*0p oftz-iyc4 z4zv/resonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it 0z ziy 4r/op4vcz-*ftwill resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standin l)mbu)uqr of5pky5.w++2 hzvg waves is 475 Hz, how far apart are two adjac 5b 5orylq +fmz+u)kv).wph2uent nodes?   m

  If two successive overtones of a vibrating string aregn+)v )8 )nmi5z 3 ildwdvcd:o 280 Hz and 350 Hz, what is the fri wd)3)n:+c o gvz dm8i)vdl5nequency of the fundamental?    Hz

  A guitar string is 90 cm zmep;6xj3*rt long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm ae r6x3mjzp*; tnd the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measuredrd)e+3 -jvdn m to vibrate at 205 Hz. By what percent should the tensionnd r+vdm j)e-3 in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measuredxtkdnw-qk9/ l12hcm5 qxtw529 hnmk-c k/ld1to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude medf1p-zx:9m +uzsaiul mf +0 0cchanical 60-Hz vibrator. The string’s mass per unit -z m+ z9a1msf0u0d+x:c plufi length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pul n4euu/3wbu 4vley. If the hanging mass m is fixed at 0.080 kg, how many differe4uveu/b n3u4w nt standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right h i6s;l3y3rsfo4 g1 jifrequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such hi134jrsfgs oi3yl6; a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes ay6poe rmdc. 6:k/;tt-l 0fcrl boundary within the Earth between two kinds of materia6. ler:-6cm0 /drp koc;ty tlfl. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the veloc m1d.-i917c; uwzu9q v hgatyn.k ep/rity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make avm .dz-9rwte7aq nu1hu1;9 iyp/ .ckg 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hinrp-j t35jex ,ts a layer of cold, dense air. If the sound wave hits3p,nx t5 -jejr the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a bounda0woz)az; kw cpm,yf/7ry between two types of rock at a f,/0) k;omcaw p7zyzw38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is abou.qq(p.4i/ xeq:c cjc pt 0.5 m in diameter. According to the user’s manual, the dish ha (x/q:p.qp.ccei4 qc js to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pacif.u:,gud;bhne-cz -i uh7tyc4 ic Ocean. As it approaches Hawaii, people observe an unusual decrease of sea uhud;-bi -c,u.n e gcyzt:h47level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant ofht4e sgf98(d v6 7jxkn 550 kN/m Find the maximum compression of the bumper if the car, with mass 150x6tjg74 vhn8ed( sf9k0 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net *pea- *)jp bwyq -h)hp18 m below, which stretches the net 1.1 m.)hp*h)a- pjpqwby*-e Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring.mo qov5s.r,9ol y+e )w The mass then falls 33 cm beforel eo9rv)so .yo,+w5mq it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), c dej)jmg0 0 syao)(yw2* uvg4fompressing the sprin4wfu )s(*ago0ymv2jj ge 0)dy g 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 c0bl(3xva2l v lm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it startxvvl (abll20 3s to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 1z70fmpl)epop5 .to 0d xd3gbn64 9foa,ce nh(0.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emittdxnf(e o0)mp5dp9b0. g4oe 6fch ,n3oltazp 7ed?    Hz

  A 2.00-kg mass vibrates according to the/u64 )qz +y b,m f0osnpuwbm;m equation x=0.650cos7.40t where x is in meters and t in seconds. Determinebn+b o ;)/fmu64zm0s wu, pyqm
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillq zmnn8gf *81iates with frequency f. What is its frequency if it accelerates atn*g fmniz88 q1 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg mad ( *zedvasj+a353ws zn stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for3s3z azv d (adesj+*w5 a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a mus3 k*ja 86he4tj2uk-ceqtxx / aical instrument are tuned to play at 392 Hz (G) and 440 Hz (A). *ta c2x4h8je/ -ktux3jqe6ak
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. lw 7k+jt1vwvnpfq d3 m01+ r4r11–33. Determine a formula (a) for the ratio of the speeds of the wave 0k wdvr41qfr7+pmw3vn+ l1jt in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and oux86lm1,y pj maq 1-sthe tip of each prong moves 1.8 mm to either sidyl1-apx1osm, u 8 qj6me of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillab+ip)s4 z-uu7 k ac,cgtes with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with wh4+biksuu - c 7g,a)cpzich the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “frcyz rt p.1w;pb188an uee” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibratioc;appnr.1bw8 8 1t yuzns of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing6)2bm ,hmbqi3ntg; dx takes mn ,;3 ib)x2q tmg6dhb1.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical directt -qjo:q-1cjs tdtf0 8 r,air*ion or can swing as a pendulum of small amplitude, t ji1at:r-r 0csq*dq-,fjt o8but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulse mfbt 70zq , 8vw1mxf*y/i qm5hbxqyt4-b )go2is generated at one end, and 20.0 ms later a second pulse is4m/)-1xtg* oybqbfyh f mt i7vq582 0,mwxqz b generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with sprin/. 7cnrs5 gu1bbjn+jtg stiffness constant k.c b1tg. u+5nr/ n7jsjb A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg rb)tq8m; ez +ncar at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table m)rt;+bzn8e q 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 / d3ofl()dru0xcgv 9z (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequencgrdz9u(vdof 0/3lxc )y of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz